Parameter uncertainty and reserve risk under Solvency II

TL;DR

This paper examines how parameter uncertainty affects reserve risk modeling under Solvency II, highlighting limitations of classical methods and proposing an improved approach that better aligns with regulatory confidence levels.

Contribution

It identifies shortcomings of traditional reserving methods for parameter uncertainty and introduces an adapted approach that achieves the desired confidence level under Solvency II.

Findings

Bootstrapping is unsuitable for modeling parameter uncertainty in this context.

The proposed method approximates the required confidence level effectively.

Classical methods may underestimate risk due to improper handling of parameter uncertainty.

Abstract

In this article we consider the parameter risk in the context of internal modelling of the reserve risk under Solvency II. We discuss two opposed perspectives on parameter uncertainty and point out that standard methods of classical reserving focusing on the estimation error of claims reserves are in general not appropriate to model the impact of parameter uncertainty upon the actual risk of economic losses from the undertakings's perspective. Referring to the requirements of Solvency II we assess methods to model parameter uncertainty for the reserve risk by comparing the probability of solvency actually attained when modelling the solvency risk capital requirement based on the respective method to the required confidence level. Using the simple example of a normal model we show that the bootstrapping approach is not appropriate to model parameter uncertainty according to this criterion. We then present an adaptation of the approach proposed in \cite {froehlich2014}. Experimental results demonstrate that this new method yields a risk capital model for the reserve risk achieving the required confidence level in good approximation.